Critical response of elastic-plastic SDOF systems with nonlinear viscous damping under simulated earthquake ground motions

Multi impulse with constant time interval is used as a representative of a long-duration earthquake ground motion. An analytical expression is derived for the elastic-plastic response of a single-degree-of-freedom (SDOF) model with nonlinear viscous damping subjected to the “critical multi impulse” which maximizes the response. The fact that only free vibration appears under such multi impulse enables the smart application of an energy approach in deriving the analytical expression for a complicated elastic-plastic response with nonlinear viscous damping. The nonlinear viscous damping characteristic for deformation is approximated in terms of a quadratic or elliptical function. The critical timing of the impulses is found to correspond to the zero restoring-force timing or the maximum velocity timing depending on the input level. It is shown that the nonlinearity in viscous damping causes a remarkable influence on the earthquake response in some cases. The reliability and accuracy of the proposed theory are investigated through the comparison with the results by the time-history response analysis to the tuned sine wave as a representative of the long-duration earthquake ground motion.